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Despite its appearance in physics around the 1850th, the second law of thermodynamics is still attracting more efforts to be clarified. More specifically, fifteen years later (1865) after its definition and introduction, entropy has been the subject of various interpretations. Hence, in physical sciences and notably in different education levels, its concept seems to be relatively tough to unambiguous decipher. In this work, we re-introduce the notion of entropy from classical, quantum and information theories viewpoints. The controversial over entropy and a measure of disorder misconception, stated by many scientists, is addressed as well to come up with less confusing physical interpretation of entropy. Hence, over time, an increase of entropy, a quantitative quantity, is most often associated to a rising of disorder, a non-quantitative quantity and no value-returning mathematical equation, rather than a continuously increasing of hidden data. In other words, linking disorder to hidden data is typically raising more confusion than clarification. Here, we shed more light on both concepts to find out an acceptable interpretation of entropy.

The notion of entropy was first introduced in 1880 by Ludwig Boltzmann [

S = k LnN (1)

where k is a constant named after Boltzmann, even though it has been introduced by Max Planck k = 1.38 10^{−23} J∙K^{−1} and N is microstates number or the probability of such a peculiar state to occur.

L. Boltzmann has desperately struggled to get his atomistic model recognized before sadly making an end to his life. This work paved a way to the statement made in 1902 by Josiah Willard Gibbs in his book [

Unlike chemists who straight forward have adopted the modern atomic model as theorized in 1808 by their British fellow John Dalton, physicists were careful patient till the apparition of solid evidences, such as A. Einstein’s theory of Brownian motion in 1905 [

δ Q T ≥ 0 (2)

where δ Q is the differential heat transfer and T is the absolute temperature at

the boundary where the heat transfer occurs and dS = δ Q T is true for a reversible process only.

Entropy is a thermodynamics property; misused sometimes as a measure of disorder [

Presumably, the observable expanding universe is not necessarily heading towards chaos even if its entropy is rising over time. 13.8 billion years ago, the big bang in this sense corresponded presumably to a minimal entropy. Entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. It can be created but not destroyed. To this end, the disorder is an unacceptable term to introduce the entropy. Various critics [

Shannon-Macmillan-Breiman found that the mathematical formula of Boltzmann defines a useful quantity in information theory. In the beginning, he was not thoroughly confident about naming this new quantity entropy [

Likewise, from a quantum physics perspective, information can never be destroyed it is conserved. This might be perceived as a paradox unless we consider the holographic principle that enables to encode three dimensions (3D) object data into two dimensions (2D). According to Max Born, a wavefunction of a system squared provides a probability to positioning a particle. From all that, detecting such a particle in many different positions might be then logically admitted unless the particle wavefunction collapses. For a particle of mass m moving in a potential V ( r → ) the wavefunction ψ ( r → , t ) is associated with De Broglie’s particle wave and a solution of the time-dependent Schrödinger’s equation:

− i h 2 π ∂ ψ ( r → , t ) ∂ t = [ − h 2 8 π 2 m ∇ 2 + V ( r → ) ] ψ ( r → , t )

It is localized in space and its mathematical expression is:

ψ ( r → , t ) = ∭ A ( k ) e − i ( k . → r → − ω t ) d k

where k is the wave vector or wavenumber; h = 6.626 10^{−34} J∙s, is a Planck constant; ω is the angular frequency; t is time and A (k) is the amplitude of the wave.

Holographic principle in this way reconciles most likely the Newtonian’s determinism and the skepticism derived from Heisenberg’s uncertainty principle, as many copies of the same 3D object can be seen in many different locations at the same time in its 2D forms.

Historically, Demon’s Laplace [

Disorder and order are not countable quantities but rather qualitative. Analogically, the observable universe expansion and increase of its entropy is subsequently a result of an extra number of microstates. Anisotropic collisions of gas atoms lead to chaotic agitations and hence loss of data.

In effect, information can be regarded as a degree of certainty or a probability that an event occurs. Lower entropy can be then correlated to how confident we are about a process to happen. As a result, a highly predictable transformation is consistent with a lower entropy. Following this logic, randomness implies higher entropy and entropy turns into an indicator of randomness or lack of confident information. It measures then the amount of the missing information.

In this sense, the second law of thermodynamics introduces the natural trend to the loss of information, for a spontaneous natural transformation.

Additionally, if disorder provides an indication of lack of pattern or an apparent missing of organization, the more precise way to measure it, seems inconvertibly controversial and unlikely to be modeled in an accurate value-returning mathematical equation. As a result, by combining both classical and quantum definitions of entropy and its definition from the theory of information perspective [

Through this work, we raised debate about a quantitative entropy and a non-quantitative disorder confusion. We concluded then that disorder might not be the more accurate information we can draw from studying entropy evolution. The entropy is not and cannot be exclusive disorder. Measuring a degree of disorder through rise of entropy is then doomed. Additionally, we showed that lack of information and loss of data would be more appropriate to describe the entropy increase. This is more relevant to provide a correct interpretation of the entropy from a thermodynamics perspective.

The authors declare no conflicts of interest regarding the publication of this paper.

Soubane, D., El Garah, M., Bouhassoune, M., Tirbiyine, A., Ramzi, A. and Laasri, S. (2018) Hidden Information, Energy Dispersion and Disorder: Does Entropy Really Measure Disorder? World Journal of Condensed Matter Physics, 8, 197-202. https://doi.org/10.4236/wjcmp.2018.84014